CK-12-Calculus

3.6. Analyzing the Graph of a Function http://www.ck12.org We note thatfis a continuous function and thus attains an absolute ma ...

http://www.ck12.org Chapter 3. Applications of Derivatives Lesson Summary We summarized the properties of functions, including ...

3.6. Analyzing the Graph of a Function http://www.ck12.org Review Questions Summarize each of the following functions by filling ...

http://www.ck12.org Chapter 3. Applications of Derivatives TABLE3.10:(continued) f(x) =^2 xx− 22 Analysis Inflection points f(x ...

3.6. Analyzing the Graph of a Function http://www.ck12.org f(x) = 1 +cosx on the interval[−π,π] TABLE3.14: f(x) = 1 +cosx Anal ...

http://www.ck12.org Chapter 3. Applications of Derivatives 3.7 Optimization Learning Objectives A student will be able to: Use ...

3.7. Optimization http://www.ck12.org We first note that since this is a real-life application, we observe that both quantities, ...

http://www.ck12.org Chapter 3. Applications of Derivatives We started with the general volume formulaV=^13 πr^2 h, but quickly r ...

3.7. Optimization http://www.ck12.org The feasible domain of this function is 0<×< 45 ,which makes sense because ifxis 45 ...

http://www.ck12.org Chapter 3. Applications of Derivatives dAdr = 4 πr− (^946) r 2 =0 whenr=^3 √ 946 4 π ≈^9 .06 cm. We note tha ...

3.7. Optimization http://www.ck12.org Review Questions In problems #1–4, find the absolute maximum and absolute minimum values, ...

http://www.ck12.org Chapter 3. Applications of Derivatives 3.8 Approximation Errors Learning Objectives A student will be able t ...

3.8. Approximation Errors http://www.ck12.org The linear approximation can be used to approximate functional values that deviate ...

http://www.ck12.org Chapter 3. Applications of Derivatives the differences between the actual and approximate values, we can ent ...

3.8. Approximation Errors http://www.ck12.org Tn(x) =f(a)+f′(a)(x−a)+f ′′(a) 2! (x−a) (^2) +...+fn(a) n! (x−a) n. We call this t ...

http://www.ck12.org Chapter 3. Applications of Derivatives We get a slightly better approximation for the quadratic than for the ...

http://www.ck12.org CHAPTER 4 Integration Chapter Outline 4.1 Indefinite Integrals Calculus 4.2 THEINITIALVALUEPROBLEM 4.3 THEAR ...

http://www.ck12.org Chapter 4. Integration 4.1 Indefinite Integrals Calculus Learning Objectives A student will be able to: Fin ...

4.1. Indefinite Integrals Calculus http://www.ck12.org With our definition and initial example, we now look to formalize the def ...

http://www.ck12.org Chapter 4. Integration ∫ exdx=ex+C. Again we could easily prove this result by differentiating the right sid ...